This invention relates generally to tomographic imaging, and more particularly to methods and apparatus for deconvolving tomographic imaging data.
In at least one known computed tomography (CT) imaging system configuration, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system and generally referred to as the xe2x80x9cimaging planexe2x80x9d. The x-ray beam passes through the object being imaged, such as a patient. The beam, after being attenuated by the object, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is dependent upon the attenuation of the x-ray beam by the object. Each detector element of the array produces a separate electrical signal that is a measurement of the beam attenuation at the detector location. The attenuation measurements from all the detectors are acquired separately to produce a transmission profile.
In known third generation CT systems, the x-ray source and the detector array are rotated with a gantry within the imaging plane and around the object to be imaged so that the angle at which the x-ray beam intersects the object constantly changes. A group of x-ray attenuation measurements, i.e., projection data, from the detector array at one gantry angle is referred to as a xe2x80x9cviewxe2x80x9d. A xe2x80x9cscanxe2x80x9d of the object comprises a set of views made at different gantry angles, or view angles, during one revolution of the x-ray source and detector. In an axial scan, the projection data is processed to construct an image that corresponds to a two-dimensional slice taken through the object. One method for reconstructing an image from a set of projection data is referred to in the art as the filtered back projection technique. This process converts the attenuation measurements from a scan into integers called xe2x80x9cCT numbersxe2x80x9d or xe2x80x9cHounsfield unitsxe2x80x9d, which are used to control the brightness of a corresponding pixel on a cathode ray tube display.
In known CT systems the x-ray beam is projected from the x-ray source through a pre-patient collimator that defines the x-ray beam profile in the patient axis, or z-axis. The collimator typically includes x-ray-absorbing material with an aperture therein for restricting the x-ray beam.
CT imaging systems typically provide image resolution within limitations imposed by such factors as collimator aperture size and slice thickness. A minimum slice thickness for at least one CT system is 1.25 millimeters, as determined primarily by detector element pitch size. In order to improve image resolution, it is desirable to reduce slice thickness to less than 1 millimeter, and to achieve such reduction with minimal impact on imaging system hardware.
It is known to reduce slice thickness by deconvolving tomographic imaging data, for example, projection data or image data, to reduce the full-width-at-half-maximum (FWHM) interval of a reconstructed slice profile. It is also known that singular value decomposition (SVD) is a matrix transform technique and can be used to arrive at a xe2x80x9cpseudo-inversexe2x80x9d to perform data deconvolution. SVD is described as follows. Let P, an n-by-1 matrix, represent a CT system slice sensitivity profile (SSP). Matrix A represents an n-by-n circular shift matrix and is derived from P using a relationship written as:             a              i        ,        j              =          p      k        ,      k    =          mod      ⁡              (                              i            +            j            +                          n              2                                ,          n                )            
where xcex1i,j are elements of A and Pk are elements of P. It is well known that, by SVD, matrix A is transformed to a product of an n-by-n column orthogonal matrix U, an n-by-n diagonal matrix W, and a transpose of an n-by-n orthogonal matrix V, i.e. using a relationship written as:
A=UWVT
Here an n-by-n matrix is used to represent A. In general, A could be an n-by-m matrix, U an n-by-l matrix, V an m-by-l matrix, and W an l-by-l matrix. For ease of illustration, an n-by-n matrix is used throughout this application.
An n-by-n deconvolution kernel matrix D is obtained using a relationship written as:
D=VWxe2x80x2UT
where Wxe2x80x2 is determined from W using a relationship written as:       W    ii    xe2x80x2    =      {                                                      1                                                W                  ii                                +                α                                      ,                                                              W              ii                         greater than             t                                                            0            ,                                    otherwise                    
where xcex1 is a regularization parameter and t is a threshold. A deconvolution kernel is obtained from matrix D. The kernel is the center column of D and thus has dimension (n, 1). The kernel is applied in imaging data deconvolution to reduce the FWHM of the imaging system SSP. Note that here only the central column is used for computational efficiency. In general, the entire matrix could be used for deconvolution.
The above-described approach, however, incorporates an assumption that the SSP, a point spread function, is to be reconstructed as a delta (impulse) function. Inflexibility of matrix inversion leaves little if any opportunity to correct for this assumption, which in many imaging applications leads to less than optimal imaging. It would be desirable to improve SVD results for use in imaging data deconvolution and thus improve image quality. It also would be desirable to make SVD more generally applicable to imaging data deconvolution.
There is therefore provided, in one embodiment, a method for deconvolving imaging data obtained in slices using an imaging system, the method including the steps of selecting a target slice sensitivity profile and determining a deconvolution kernel using the target slice sensitivity profile. The above-described method allows an imaging system user to use singular value decomposition to achieve a desired slice sensitivity profile through imaging data deconvolution. Thus sub-millimeter slice thickness and improved image resolution are achieved without having to modify hardware in existing imaging systems.